Asset Pricing: A Tale of Two Days

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1 Aet Pricing: A Tale of Two Day Pavel Savor y Mungo Wilon z Thi verion: June 2013 Abtract We how that aet price behave very di erently on day when important macroeconomic new i cheduled for announcement relative to other trading day. In addition to igni cantly higher average return for riky aet on announcement day, return pattern are alo much eaier to reconcile with tandard aet pricing theorie, both cro-ectionally and acro time. On uch day, tock market beta i trongly related to average return. Thi poitive relation hold for individual tock, for variou tet portfolio, and even for bond and currencie, uggeting that beta i after all an important meaure of ytematic rik. Furthermore, a robut rik-return trade-o exit on announcement day. Expected variance i poitively related to future aggregated quarterly announcement day return, in contrat to market or aggregated non-announcement day return where there i no evidence of predictability. We explore the implication of our nding in the context of variou aet pricing model. Thi paper wa previouly circulated under the title "Stock Market Beta and Average Return on Macroeconomic Announcement Day." y (215) The Wharton School, Univerity of Pennylvania. z Said Buine School and Oxford-Man Intitute, Oxford Univerity. We thank John Campbell, Ralph Koijen, Juhani Linnainmaa, Chritopher Polk, Rob Stambaugh, Stephanie Sike, Amir Yaron, and eminar participant at the 2013 American Finance Aociation Annual Meeting, 2013 Adam Smith Workhop in Aet Pricing (Univerity of Oxford), 5th Annual Florida State Univerity SunTrut Beach Conference, Dartmouth College (Tuck), Norwegian School of Economic, Temple Univerity (Fox), Acadian Aet Management, Quantitative Management Aociate, and SAC Capital Advior for their valuable comment. 1

2 Introduction Stock market beta hould be important determinant of rik premia. However, mot tudie nd no direct relation between beta and average exce return acro tock. 1 Over time, expected return hould depend poitively on market rik, mot often proxied for by ome meaure of expected market volatility, but uch a relation ha not yet been concluively documented. In thi paper, we how that for an important ubet of day tock market beta actually i trongly related to return, and a robutly poitive rik-return trade-o alo exit on thee ame day. Speci cally, on day when new about in ation, unemployment, or Federal Open Market Committee (FOMC) interet rate deciion i cheduled to be announced (hereinafter, announcement day or a-day ), tock market beta i economically and tatitically igni - cantly related to return on individual tock. Thi relation alo hold for portfolio containing tock orted by their etimated beta, for the 25 Fama-French ize and book-to-market portfolio, for indutry portfolio, and even for aet other than equitie, uch a government bond or currency carry-trade portfolio. The relation between beta and expected return i till igni cant controlling for rm ize and book-to-market ratio, and alo controlling for beta with the ize, value, and momentum factor. The aet pricing retriction implied by the mean-variance e ciency of the market portfolio (ee, e.g., Cochrane (2001), chapter 1.4) appear to be ati ed on announcement day: the intercept of the announcement day ecuritie market line (SML) for average exce return i either very low or not igni cantly di erent from zero, and it lope i not igni cantly di erent from the average announcement day tock market exce return. By contrat, beta i unrelated to average return on other day ( non-announcement day or n-day ), with the implied market rik premium typically being negative. Our main nding i ummarized in Figure 1. We etimate tock market beta for all tock uing rolling window of 12 month of daily return from 1964 to We then 1 Seminal early tudie include Black, Jenen, and Schole (1973), Black (1972), Fama and French (1992), and Black (1993). Polk, Thomon, and Vuolteenaho (2005) i a more recent paper. 2

3 ort tock into one of ten beta-decile value-weighted portfolio. Figure 1 plot average realized exce return for each portfolio againt average portfolio beta eparately for nonannouncement day (blue point and line) and announcement day (red point and line). 2 The non-announcement day point how a negative relation between average return and beta: an increae in beta of one i aociated with a reduction in average daily exce return of about 1.5 bai point (bp), with a t-tatitic for the lope coe cient etimate above three. [FIGURE 1 ABOUT HERE] In contrat, on announcement day the relation between average return and beta i trongly poitive: an increae in beta of one i aociated with an increae in average exce return of 10.3 bp. The relation i alo very tatitically igni cant, with a t-tatitic of over 13. Furthermore, the R 2 of each line are repectively 63.1% for non-announcement day and 95.9% for announcement day. For the beta-orted portfolio, almot all variation in announcement day average exce return i explained jut by variation in market beta. Thee reult ugget that beta i after all an important meaure of ytematic rik. At time when invetor expect to learn important information about the economy, they demand higher return to hold higher beta aet. Moreover, earlier reearch etablihe that thee announcement day repreent period of much higher average exce return and Sharpe ratio for the tock market and long-term Treaury bond. Savor and Wilon (2013) (SW) nd that in the period the average exce daily return on a broad index of U.S. tock i 11.4 bp on announcement day veru 1.1 bp on all other day. The non-announcement day average exce return i actually not igni cantly di erent from zero, while the announcement day premium i highly tatitically igni cant and robut. Thee etimate imply that over 60% of the equity rik premium i earned on announcement day, which contitute jut 13% of the ample period. 3 SW further how that the volatility of announcement day return i 2 Note that in Figure 1 the beta for each portfolio are the ame on both kind of day; only the average realized exce return are di erent. 3 Lucca and Moench (2011) con rm thee reult in the pot-1994 period for pre-cheduled FOMC announcement, with the etimated hare of the announcement day cumulative return increaing to over 80% 3

4 only lightly higher, o that the Sharpe ratio of announcement day return i an order of magnitude higher. 4 Therefore, invetor are compenated for bearing beta rik exactly when rik premia are high. One potential alternative explanation for our reult i that there i nothing pecial about announcement day per e, but rather that the trong poitive relation between beta and return documented on uch day i actually driven by ome particular feature of announcement day that i alo hared by other day. However, we do not nd evidence upporting thi alternative hypothei. We how that no imilar relation exit on day when the tock market experience large move, or on thoe day when average market return are much higher than the ample mean (more peci cally, during the month of January or during the turn of the month). We next how that expected variance forecat quarterly aggregated announcement day return (with a large poitive coe cient and a t-tatitic above four), which i conitent with a time-erie trade-o between rik and expected return. 5 Expected variance, which hould repreent a good proxy for market rik, i by far the mot important factor for predicting return on announcement day. Thi reult i very robut, holding in a variety of VAR peci cation, when we ue weighted leat quare, and alo when we divide our ample into two halve. By contrat, on other day there i no evidence of uch predictability, with a coe cient on expected variance that i actually negative and not tatitically igni cant. Combined with our previou nding on market beta, thi reult highlight an important puzzle. Two major prediction of tandard aet pricing theorie hold on thoe day when certain important macroeconomic information i cheduled for releae, which are alo characterized by very high rik premia. On day without announcement, however, there i no upport for either hypothei (if anything, for market beta the relation with return i in thi more recent period. In the ample period conidered in thi paper, the correponding hare i over 70%. 4 They rationalize uch a di erence with an equilibrium model in which agent learn about the expected future growth rate of aggregate conumption mainly through economic announcement. 5 We thank John Campbell, Stefano Giglio, Chritopher Polk, and Robert Turley for providing u with their data. 4

5 the oppoite of what theory predict). Any complete theory thu would have to explain both why market beta determine expected return on announcement day and why they do not on other day. Deepening the puzzle, we nd little di erence between market beta acro di erent type of day. We how formally that, to the extent that the Capital Aet Pricing Model (CAPM) doe not hold on non-announcement day for aet with identical beta on both type of day, no unconditional two-factor model can be conitent with our reult. Moreover, a ucceful theory would alo have to argue why higher expected rik reult in higher expected return on announcement day when there i no uch rik-return trade-o on other day. Our reult have an analogue in the reearch that etablihed potentially puzzling relationhip between average return and tock characteritic. 6 Intead of examining how expected return vary with tock characteritic, we invetigate how tock return vary with type of information event. 7 Our main nding i that cro-ectional pattern and the nature of the aggregate rik-return trade-o are completely di erent depending on whether there i a pre-cheduled releae of important macroeconomic information to the public. 8 The challenge for future reearch i to reconcile the two et of relationhip. Announcement day matter becaue for many riky aet, including the aggregate tock market and long-term government bond, return on thoe day account for a very large portion of their cumulative return. Furthermore, there exit a clear link between macroeconomic rik and aet return on thoe day. Finally, non-announcement day contitute the great majority of trading day in a given year, and conequently alo cannot be ignored. A good theory hould explain both where the majority of cumulative return come from and what happen mot of the time. The ret of the paper i organized a follow: Section I decribe our reult on the relation 6 A early example of thi literature, ee Bau (1983), Chan, Chen, and Hieh (1985), Chan and Chen (1991), and Fama and French (1996). 7 Balduzzi and Moneta (2012) ue intra-day data to meaure bond rik premia around macroeconomic announcement, and are imilarly unable to reject a ingle-factor model at high frequency. 8 We are agnotic about the exact nature of the new coming out on announcement day, merely auming that it i re ected in return, and that market beta are therefore poibly the relevant meaure of ytematic rik on uch day. 5

6 between beta and return on announcement and non-announcement day; Section II how evidence on the rik-return trade-o on each type of day; Section III explain why our reult are hard to reconcile with everal prominent model and dicue avenue for future reearch that could potentially explain the di erence between announcement and non-announcement day; and Section IV conclude. In the Appendix, we preent a formal argument illutrating how no unconditional two-factor model can explain the cro-ection of expected return on both type of day. I. Beta on Announcement and Non-announcement Day I.A. Data and Methodology We obtain tock and Treaury bond return data from CRSP. Our main tock market proxy i the CRSP NYSE/AMEX/NASDAQ value-weighted index of all lited hare. We obtain return for the 25 ize- and book-to-market-orted portfolio and the 10 indutry portfolio from Kenneth French webite. We etimate a tet aet tock market beta (and other factor beta) over rolling one-year window uing daily return. 9 We meaure a tock log market capitalization (ME) and book-to-market (BM) a in Fama and French (1996). The ample cover the period. Our macroeconomic announcement date are the ame a in SW. In ation and unemployment announcement date come from the Bureau of Labor Statitic webite, where they become available tarting in We ue Conumer Price Index (CPI) announcement before February 1972 and Producer Price Index (PPI) thereafter (a in SW), ince PPI number are alway releaed a few day earlier, which diminihe the new content of CPI number. The date for the FOMC cheduled interet rate announcement date are available from the Federal Reerve webite from Uncheduled FOMC meeting are not included in the ample. We rt preent reult uing the claic two-tep teting procedure for the CAPM, which 9 All our nding remain the ame if we intead etimate beta over 5-year period uing monthly return. They alo do not change if we ue Schole-William beta. 6

7 we employ for tock portfolio orted on market beta, indutry, ize, and book-to-market, and for Treaury bond and currency carry-trade portfolio. For the econd tage regreion, we adopt the Fama-MacBeth procedure, and compute coe cient eparately for announcement and non-announcement day. More peci cally, for each period we etimate the following cro-ectional regreion: R N j;t+1 R N f;t+1 = N 0 + N 1 b j;t (1) and R A j;t+1 R A f;t+1 = A 0 + A 1 b j;t ; (2) where b j;t i tet aet j tock market beta for period t (etimated over the previou year uing daily return) from the rt-tage regreion, R N j;t+1 R N f;t+1 i the exce return on the tet aet on n-day, and R A j;t+1 R A f;t+1 i the exce return on the tet aet on a- day. We then calculate the ample coe cient etimate a the average acro time of the cro-ectional etimate, and the tandard error equal the time-erie tandard deviation of the cro-ectional etimate divided by the quare root of the repective ample length. 10 Uing thi method, we can tet whether the di erence in coe cient etimate i tatitically igni cant by applying a imple t-tet for a di erence in mean. In addition to Fama-MacBeth run eparately for announcement and non-announcement day, we alo etimate a ingle regreion and directly tet whether beta coe cient (implied rik premia) are di erent on a-day and n-day. Speci cally, we etimate the following panel regreion: R j;t+1 R f;t+1 = 0 + 1j;t b + 2 A t+1 + 3j;t b A t+1 ; (3) where A t+1 i a determinitic indicator variable that equal one if day t+1 i an announcement day and zero otherwie. Standard error are then clutered by time to adjut for the cro- 10 Thi approach provide tandard error that re ect cro-ectional correlation of the reidual acro tock. We do not correct the tandard error for potential autocorrelation of the cro-ectional etimate, becaue our analyi indicate thoe are not igni cant enough to have a material impact. 7

8 ectional correlation of the reidual. I.B. Beta-orted Portfolio Table 1 report reult for portfolio orted on tock market beta, which are rebalanced each month. We etimate beta for each individual tock uing one year of daily return, ort tock into decile according to thi beta, and then etimate each portfolio beta uing one year of daily return. We report reult for both value-weighted and equal-weighted portfolio. In Panel A, we etimate equation (1) and (2) uing the Fama-MacBeth approach, and how that for value-weighted return on non-announcement day the intercept N 0 equal 2.0 bp (t-tatitic = 3.6) and the lope of the SML N bp (t-tatitic = -0.9), implying a negative equity rik premium. The average R 2 for the cro-ectional regreion i 49.2%. [TABLE 1 ABOUT HERE] The picture i very di erent on announcement day. The intercept i 1.3 bp and i not igni cantly di erent from zero. The lope of the SML i 9.2 bp (t-tatitic = 2.8), and it i not igni cantly di erent from the average announcement day market exce return of 10.5 bp (the t-tatitic for the di erence i 0.5). And the average R 2 i now 51.4%. The fact that the intercept i not tatitically di erent from zero and that the implied rik premium i very cloe to the oberved rik premium addree the critique by Lewellen, Nagel, and Shanken (2010), who ugget that aet pricing tet focu on the implied rik premium and intercept in cro-ectional regreion and not jut on R 2. A tet for di erence acro regime, which i a imple t-tet comparing mean between the announcement-day and non-announcementday ample, implie that the lope coe cient i 10.3 bp higher on a-day, with a t-tatitic of 2.9. The intercept are not igni cantly di erent. We alo ue a boottrap to etimate tandard error for R 2 on non-announcement day, and nd that the announcement-day R 2 i outide the 95% con dence interval. The reult are imilar for equal-weighted portfolio: the lope i igni cantly negative on non-announcement day (-3.1 bp, with a t-tatitic of -2.8) and igni cantly poitive (and 8

9 not tatitically ditinguihable from the average announcement-day market exce return) on announcement day (9.4 bp, with a t-tatitic of 3.0). Both intercept are now poitive and igni cant. The lope coe cient i igni cantly higher on announcement day, with a di erence of 12.6 bp (t-tatitic = 3.6). In Panel B, we apply a pooling methodology to etimate the di erence in the intercept and lope coe cient in a ingle regreion uing all day, and obtain the ame reult a thoe in Panel A. The regreion peci cation i given by equation (3), and t-tatitic are computed uing clutered tandard error. For value-weighted portfolio, the n-day intercept equal 2.4 bp (t-tatitic = 3.3), and i 1.6 bp higher (but not igni cantly o) on a-day. The n-day lope coe cient equal -1.5 bp (t-tatitic = -1.2) on n-day, and i igni cantly higher on a-day, with a di erence of 8.4 bp (t-tatitic = 2.7). The non-igni cance of the announcement-day indicator on it own i alo noteworthy, ince in the abence of the interaction term it i highly poitive and igni cant. Thu, all of the outperformance of di erent beta-orted portfolio on a-day i explained by their beta. For equal-weighted portfolio, we get imilar reult. The n-day intercept i 7.9 bp (ttatitic = 10.6), which i 6.1 bp lower than the intercept on a-day (t-tatitic = 3.0). The n-day lope coe cient i -3.9 bp (t-tatitic = -2.9), and the a-day lope coe cient i 11.9 bp higher, with a t-tatitic for the di erence of 3.6. Figure 1 plot average realized exce return for ten beta-orted portfolio againt average portfolio beta eparately for non-announcement day and announcement day (dicued in the Introduction). 11 A a robutne check, Figure 2 chart the ame variable for 50 betaorted portfolio, with very imilar nding. On non-announcement day, the intercept i poitive and igni cant (2.5 with a t-tatitic of 11.7), while the beta coe cient i negative and igni cant (-1.4 with a t-tatitic of -6.5). In contrat, on announcement day the intercept i not igni cantly di erent from zero (-0.8 with a t-tatitic of -1.5), and the beta coe cient i poitive and igni cant (10.4 with a t-tatitic of 18.5), and almot the ame a the average how. 11 Note that for eae of expoition the x-axi doe not alway interect the y-axi at zero in the gure we 9

10 announcement-day market exce return. Very intriguingly, the highet-beta portfolio ha the lowet n-day return (-1.9 bp) and alo the highet a-day return (22.7 bp), o that the very ame portfolio exhibit very di erent performance on di erent type of day. [FIGURE 2 ABOUT HERE] One potential worry i that our reult are biaed by uing beta that are not conditioned on the type of day. However, when we etimate beta eparately for announcement and non-announcement day, we nd very mall di erence between the two beta for all of our tet portfolio. We preent thee reult below, which trongly ugget that di erence in market beta for individual tock and variou tet portfolio on announcement and nonannouncement day do not account for our reult. Intead, it i the di erence in average realized exce return that drive our nding. I.C. Book-to-Market and Size, Indutry, Bond, and Carry Portfolio Figure 3 preent analogou reult to thoe in Figure 1 and 2 for the 25 ize- and book-tomarket-orted portfolio. For non-announcement day return, the blue point replicate the tandard nding that beta are unable to price thee portfolio. In particular, tock with higher beta have lower average return. The blue line i the tted value of equation (1), in which tock market beta i found to command a negative rik premium (-5.2 bp, with a t-tatitic of 3.9). [FIGURE 3 ABOUT HERE] The red point give the average announcement day exce return for the ame portfolio, plotted againt the ame beta. Now again the prediction of the CAPM hold almot perfectly: the (red) etimate of the announcement-day ecuritie market line ha an intercept of 0.4 (t-tatitic=0.3) and a lope of 10.7 (t-tatitic=8.5), which i very cloe to the etimated announcement-day tock market rik premium of 10.5 bp. The R 2 equal 75.9%, indicating that mot of the variation in average exce return of the 25 Fama-French portfolio on announcement day i accounted for by their tock market beta Market beta do not help explain the cro-ection of momentum portfolio return on either announce- 10

11 We further how below that almot all cumulative return of growth tock, mall tock, and the market itelf are earned on announcement day. By contrat, although all portfolio earn higher return on announcement day, value tock earn a ubtantial amount of their total return on non-announcement day. Figure 4 how the ame chart for ten indutry portfolio. Once again, the blue point lie around a at or mildly downward-loping line with a poitive intercept, and we are unable to reject a zero or negative relationhip between the tock market beta and average return, with a lope of -1.3 (t-tatitic = -1.6). In contrat, the red point lie cloely around an announcement-day SML, whoe lope i etimated to equal 7.2 (t-tatitic=2.5). [FIGURE 4 ABOUT HERE] We next repeat the ame analyi for all of our equity portfolio together (ten beta-orted, 25 Fama-French, and ten indutry portfolio). Since the variou contituent portfolio are formed according to very di erent characteritic, thi i a very tringent and important tet con rming the robutne of our reult. Figure 5 provide the beta / average return chart for the 45 tet portfolio, while Table 2 report coe cient etimate for Fama-MacBeth (Panel A) and pooled regreion (Panel B) for thee tet aet combined. Figure 5 look about the ame a our previou chart. On n-day, the intercept i poitive and igni cant (3.3 bp with a t-tatitic of 5.4), the lope coe cient i negative and igni cant (-1.7 bp with a t-tatitic of -2.9), and the R 2 i 16.2%. On the other hand, on a-day the intercept i not igni cantly di erent from zero (-0.4 with a t-tatitic of -0.5), the lope coe cient i poitive and igni cant (10.9 bp with a t-tatitic of 12.6), and extremely cloe to the ample average a-day market return, and the R 2 i 78.7%. A before, market beta explain mot of the cro-ectional return variation on announcement day, while on non-announcement day they actually predict lower return for higher-beta aet. [FIGURE 5 ABOUT HERE] In Panel A of Table 2, on a-day the implied rik premium i etimated to be 8.7 bp ment or non-announcement day. 11

12 (t-tatitic = 2.7), while the n-day lope i negative and inigni cant (-1.4 with a t-tatitic of -1.3). The di erence in the lope coe cient i 10.1 bp (t-tatitic = 3.0), indicating that beta i much more poitively related to average return on a-day. Thi reult i con rmed by the pooled regreion in Panel B, where the lope on n-day i lightly negative (-1.4, which i the ame a in the Fama-MacBeth regreion), but i 4.5 bp higher on a-day (t-tatitic = 4.1). In thi regreion, a-day beta doe not quite drive out the a-day indicator e ect, which indicate that, even controlling for beta, a-day return are 5.2 bp higher (t-tatitic = 2.0). [TABLE 2 ABOUT HERE] Figure 6 plot etimate of average exce return againt beta for government bond with maturitie of 1, 5, 7, 10, 20, and 30 year. The blue line how a completely at SML indicating a zero relation between beta and average exce return. In contrat, the red point lie cloely around an announcement-day SML, whoe lope i etimated to equal 6.2 (t-tatitic=4.4) for bond. 13 [FIGURE 6 ABOUT HERE] Finally, market beta are poitively related to return even for currency carry-trade portfolio. In Figure 7, we plot the average daily return to the currency-only component of ve carry-trade portfolio (P1 through P5) from November 1983 to December 2011, eparately for a-day and n-day. The portfolio are formed a follow: every day we allocate currencie to ve foreign exchange portfolio uing their one-month forward premia (P1 contain lowet-yielding currencie and P5 highet-yielding currencie), and then the next day, within each baket, we take a imple average of the log exchange rate return only. Data cover the 20 mot liquid developed and emerging market currencie (25 before the introduction of the euro). Our approach i the ame a in Della Corte, Riddiough, and Sarno (2012). 14 The high-yielding currencie in P5 uually depreciate relative to the low-yielding currencie in P1, but, a i well known, not by enough on average to o et the di erence in yield, o that the 13 The implied rik premium for bond i biaed upward, ince SW how that market beta of bond (unlike our nding for tock) are igni cantly higher on announcement day relative to non-announcement day. 14 We thank Paquale della Corte for providing u with their data on daily portfolio exchange-rate return component. 12

13 return to the currency carry trade are on average poitive. A hown in Figure 7, while on non-announcement day the tandard pattern, where low-yield currencie tend to appreciate and high-yield currencie tend to depreciate, hold, on announcement day the revere i true: low-yield currencie depreciate and high-yield currencie appreciate. The average exchange-rate component of the return on P5 minu P1 i thu negative on n-day but poitive on a-day. The di erence between a-day and n-day return i 5.0 bp per day and i tatitically igni cant (t-tatitic = 2.2). Figure 7 plot the average exchange-rate component of return for the ve carry-trade portfolio on the y-axi and their market beta on the x-axi. A before, we nd virtually no di erence between portfolio beta acro di erent type of day. On n-day, the relation between average exchange-rate return and market beta i negative, and both economically and tatitically igni cant. On a-day the relationhip revere, and become trongly poitive, with an economically and tatitically igni cant lope acro the ve portfolio. Thu, the pattern we previouly document in the paper for variou tock portfolio and for government bond alo appear to hold for foreign exchange rate: high-yield currencie earn higher return on a-day, conitent with their market beta, while low-yield beta earn lower average return, alo conitent with their beta. [FIGURE 7 ABOUT HERE] I.D. Individual Stock Our reult o far how that on announcement day market beta are trongly poitively related to return for a variety of tet aet, including variou tock portfolio, government bond of di erent maturitie, and carry-trade currency portfolio. We next evaluate the ability of beta to explain return on announcement day for individual tock. In Table 3, we run Fama-MacBeth (a before, eparately for a- and n-day) and pooled regreion of realized exce return on a rm tock market beta. In Panel A and B, we include a control rm ize, book-to-market ratio (the two characteritic identi ed by Fama and French (1992) a 13

14 helping explain the cro-ection of average tock return), and pat one-year return; and in Panel C and D our control are a rm beta with the Fama-French mall-minu-big (SML), high-minu-low (HML), and the Carhart up-minu-down (UMD) factor. The ample cover all CRSP tock for which we have the neceary data. In Panel A, we ee that non-announcement day are conitent with the tandard reult: ize i trongly negatively related to average return, book-to-market i trongly poitively related, and beta i not igni cantly related. (Pat one-year return i negatively related to non-announcement day return, but i barely igni cant.) By contrat, on announcement day market beta i trongly related to return. The coe cient etimate i 7.2 bp, with a t-tatitic of 3.3. The di erence between a- and n-day beta coe cient i 8.1, and i tatitically igni cant (t-tatitic = 3.5). Both the implied a-day market rik premium and the di erence between a- and n-day rik premia are omewhat lower than thoe in Table 1 and 2, mot likely becaue individual tock beta are etimated with more meaurement error than thoe for portfolio. The ize coe cient on a-day remain economically and tatitically trongly igni cant, while the book-to-market one become le important, no longer tatitically igni cant and with it magnitude dropping by more than 50%. Beta appear to be identifying variation in expected return independent of variation explained by other characteritic: the beta coe cient i imilar when only beta i included in the regreion, while the coe cient on rm characteritic are imilar when only characteritic are included. Thee reult ugget that on announcement day beta identi e ource of expected return unrelated to ize, book-to-market, and pat return. The nding continue to hold for a pooled regreion with an a-day dummy and the interaction between the dummy and market beta, and are preented in Panel B. [TABLE 3 ABOUT HERE] In Panel C and D, we add factor beta a control intead of rm characteritic. With the Fama-MacBeth approach (Panel C), on n-day tock return are negatively related to market beta, with a coe cient of -2.5 bp and a t-tatitic of 3.5, and poitively related to 14

15 SMB and HML beta, a i tandard. On a-day, individual tock return are poitively related to market beta, with a coe cient of 4.2 bp (t-tatitic = 2.0), and the 6.6 bp di erence relative to n-day i trongly igni cant (t-tatitic = 3.1). Stock return are till poitively related to SMB beta on a-day, but are no longer igni cantly related to HML beta. Interetingly, although return are negatively related to UMD beta on both type of day, the coe cient i igni cant only on a-day. A before, thee reult do not change when we ue a ingle pooled regreion (Panel D). We conclude that the trong poitive relation between market beta and return on a-day hold even for individual tock, depite the fact that meaurement error in individual tock beta probably make it much harder to detect uch a relation. I.E. Large Abolute Return or Announcement Day Return? One poible explanation for our nding i that announcement day may be time of large market move and that tock with higher beta co-move more with the market on thee large-move (intead of announcement) day, generating a purely mechanical ucce for tock market beta. In other word, it may be the cae that market beta are related to return on announcement day olely becaue thee day are more likely to be period of extreme market movement and not becaue announcement day are fundamentally di erent in any other way. To addre thi poibility, we etimate ecuritie market line for day of large market return (de ned a abolute return in the top decile) for the 25 Fama-French portfolio. We nd that the relationhip between beta and average return on uch day i actually trongly negative, with an implied rik premium of bp (t-tatitic = -7.5). Thi implied rik premium i much lower than the average return on large-move day, which equal bp. We can thu reject thi alternative explanation. Furthermore, SW how that the volatility of market return i not much greater in magnitude on announcement day. Intead, it i the market Sharpe ratio that i much higher on uch day. [FIGURE 8 ABOUT HERE] 15

16 I.F. High Average Return or Announcement Day Return? Another potential explanation i that our reult are not driven by announcement day but rather more generally by period when rik premia are higher. In other word, it could be the cae that market beta help explain the cro-ection of return much better during thoe period when the equity rik premium i high, 15 and that our nding re ect thi relation rather than omething that i peci c to announcement day. One way to addre thi alternative i to identify other recurring and predictable period when the market rik premium i igni cantly higher than the average, and explore the relation between beta and return during uch period. Baed on prior work, we ugget two candidate period: the month of January and the turn of the month. 16 Starting with Roze and Kinney (1976), a large body of work document high tock return in January. Ariel (1987) and Lakonihok and Smidt (1988) how that tock return are on average epecially high during the turn of the month, typically de ned a the lat trading day of a month plu the rt four trading day of the following month. Figure 9 and 10 how that the January and the turn-of-the-month e ect are roughly comparable to announcement day, both in term of average exce return and Sharpe ratio. Of coure, it could be the cae that thee phenomena imply repreent anomalie or artifact of the data rather than genuinely higher rik premia, but we ignore thi iue for the purpoe of our tet. [FIGURES 9 AND 10 ABOUT HERE] In Figure 11, we how that for the 25 Fama-French portfolio market beta are only very weakly related to average return during the turn-of-the-month period. The implied rik premium i poitive, but it i quite low (1.9 bp relative to the average turn-of-the-month return of 8.5 bp) and not tatitically igni cant (t-tatitic = 0.7). Furthermore, the R 2 for the regreion of average exce return on market beta i only 2.2%. The implied rik premium during January, hown in Figure 12, i ubtantially higher (9.6 bp), but it i not tatitically igni cant (t-tatitic = 1.1). Moreover, market beta explain only a very mall 15 A an extreme example, if the rik premium i zero, market beta hould obviouly not forecat return. 16 We thank Ralph Koijen for uggeting the turn-of-the-month e ect. 16

17 fraction of cro-ectional return variation during that month, with an R 2 of 5.2%. To um up, in contrat to announcement day, the beta-return relation i not trongly poitive during thee other period of high average market return, and thu we conclude that our reult are peci c to announcement day rather than generally holding for any high-return period. [FIGURES 11 AND 12 ABOUT HERE] I.G. Average Return and Cumulative Return Share In thi ection, we compare the average realized exce return on announcement and nonannouncement day. Table 4 report thee average return for the 25 ize- and book-to-market orted portfolio in Panel A, for the market, SMB, HML, and UMD factor in Panel B, for the ten beta-orted portfolio in Panel C, and for the ten indutry portfolio in Panel D. The rt obviou feature of the table i that all portfolio return are much higher on announcement day. If thee average exce return correpond to rik premia, then thi fact indicate that all portfolio are expoed to announcement-day rik. [TABLE 4 ABOUT HERE] The econd point i that for many tet aet the pattern of average exce return are revered on announcement day. Panel A how that on non-announcement day the value portfolio outperform the growth portfolio for each ize quintile (the well-known value premium). On announcement day, however, the low book-to-market portfolio actually outperform the high book-to-market portfolio. The pattern i pretty nearly monotonic except for the extreme value tock. The factor HML return i poitive and tatitically igni cant on non-announcement day, but negative and inigni cant on announcement day (Panel B). Thu, the tandard value-beat-growth pattern i revered on announcement day when the market rik premium and Sharpe ratio are much higher. Furthermore, mall rm tock do not outperform big rm tock on non-announcement day - all of the well-known outperformance of mall tock occur on announcement day. 17

18 The return on the SMB factor i baically zero on non-announcement day (a it i for the extreme growth portfolio) and very high on announcement day. Interetingly, momentum alo outperform by a factor of nearly two on announcement day (although the return to UMD are till trongly igni cant on non-announcement day), uggeting that part of momentum i explained by the ame phenomenon. In Panel C, we can ee the return pattern i alo revered for beta-orted portfolio. For example, the highet-beta decile u er the lowet n-day exce return (which i actually negative) of all ten portfolio, but enjoy by far the highet a-day return (16.7 bp). Similarly, a Panel D how, high-tech tock have the lowet n-day exce return (1.0 bp) and the highet a-day return (13.0 bp) of all indutry portfolio. In ummary, Table 4 how that the following aet do well on announcement day and otherwie earn very low average exce return: the market, mall tock, growth tock, and high-beta tock. Previou work by SW how that long-term bond alo earn mot of their annual exce return on announcement day (and thi relation i increaing with bond maturity). All other portfolio alo earn igni cantly higher return on announcement day, but their relative return (with repect to other day) are le remarkable. In order to further demontrate the importance of announcement day for performance of variou tet aet, in Table 5 we provide the implied hare of cumulative exce return that are earned on thee day. Speci cally, we de ne the hare a having a numerator equal to the log mean exce return on a-day time the number of a-day. The denominator i the um of the log mean exce return on a-day time the number of a-day and the log mean exce return on n-day time the number of n-day. Campbell and Viceira (2002) (chapter 2) note that a buy-and-hold invetor maximizing expected CRRA utility of terminal wealth and allocating wealth between a rikle aet and a riky aet hould et hi hare in the riky aet proportional to the log average, and therefore thi (rather than the mean exce return) eem the more appropriate meaure for uch an invetor. Our reult are quite imilar uing 18

19 jut mean exce return. 17 The rt panel of Table 5 how the hare for the 25 Fama-French ize- and bookto-market-orted portfolio. Small growth ha a negative average exce return on n-day and a negative overall exce return (meaning that it underperformed the rik-free aet over the ample period), but a poitive (and high) average exce return on a-day. In conequence, the a-day cumulative return i minu 355% of the total cumulative return. Obviouly, in cae of negative total exce return, the magnitude of our meaure i not overly meaningful, but the general point i that mall growth tock were a very bad invetment, except, crucially, on a-day. The next two mall-cap growth portfolio alo have negative n-day average exce return but overall poitive exce return, o the a-day cumulative return are repectively 187% and 156% of the total return. A-day return account for the majority of cumulative return for all portfolio in the lowet two book-to-market quintile and alo for the mallet and larget of the median book-to-market portfolio. The implied hare monotonically decline with book-to-market o that value portfolio earn a maller hare of total return on a-day than growth portfolio, but even mall and large value earn 37% and 50% repectively of their cumulative return on a-day, which account for only 11.3% of trading day. For beta-orted portfolio, the hare i not monotonic in beta but U-haped. For the lowet-beta portfolio, the a-day hare i 61%, declining to 25% for the third-lowet beta portfolio. It then almot monotonically increae to 49% for the 6th beta portfolio, 48% for the 7th beta portfolio, 87% for the 8th beta portfolio, 155% for the 9th (which ha a negative n-day average exce return but poitive overall exce return), and an enormou -575% for the highet beta portfolio (which ha a negative n-day and overall exce return). [TABLE 5 ABOUT HERE] 17 The hare of compounded exce return that i actually earned on a-day i di cult to interpret. For example, an invetor borrowing $1 at the rik-free rate to nance a $1 long poition in the market at the beginning of 1964, and rolling over every day, would have $ by the end of If he had done o only on a-day, he would have $5.67, and if only on n-day, $ Both the compounded a-day return and the compounded n-day return are igni cantly le than the total compounded return, o that the um of the hare of the total return earned on a- and n-day i much le than one. 19

20 The table alo report hare for indutry-orted portfolio, which range from 31% for non-durable to 101% for high-technology rm and 106% for durable. The hare of market return earned on a-day implied by our etimate i 74%. Taken together the number how that for all tet aet a igni cant fraction of their total return i earned on a-day, which contitute jut 11.3% of the ample. The lowet fraction i 25% for the third-lowet beta decile portfolio, followed by 31% for non-durable. For all other portfolio, at leat one third of their total return are earned on a-day. For about half of the tet aet, the majority of return are earned on a-day, and for the market, growth tock, high-beta tock, and tock in cyclical indutrie an overwhelming majority i earned on a-day. I.H. Announcement Day veru Non-announcement Day Beta Our analyi above ue the ame beta for each tet aet on both announcement and nonannouncement day (i.e., we etimate beta uing all day, without ditinguihing between a- and n-day). One potential worry i that our reult may be biaed by thi approach, where beta are not conditioned on the type of day. For example, di erent a-day and n-day beta could potentially help explain the di erence in average return that we document. In order to examine thi hypothei, we now compute beta eparately for announcement and non-announcement day. Table 6 preent the di erence between beta etimated eparately for a-day and n-day (together with the n-day beta, a a reference point). For the ten beta-orted portfolio (Panel A), the di erence i not tatitically igni cant for any of the portfolio, with the larget di erence equaling For the Fama-French 25 portfolio (Panel B), the di erence i igni cant for only ix (motly mall-cap) portfolio, and the magnitude i never too large. The larget di erence i for the mall value portfolio, where it i higher on n-day, which i a 10% relative di erence. Thee magnitude are too mall to be a igni cant factor in explaining the very large di erence in average return pattern between a-day and n- 20

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